/home/ntakagi/work/STLport-5.1.5/src/complex.cpp Go to the documentation of this file. /* * Copyright (c) 1999 * Silicon Graphics Computer Systems, Inc. * * Copyright (c) 1999 * Boris Fomitchev * * This material is provided "as is", with absolutely no warranty expressed * or implied. Any use is at your own risk. * * Permission to use or copy this software for any purpose is hereby granted * without fee, provided the above notices are retained on all copies. * Permission to modify the code and to distribute modified code is granted, * provided the above notices are retained, and a notice that the code was * modified is included with the above copyright notice. * */ #include "stlport_prefix.h" #include <numeric> #include <cmath> #include <complex> #if defined (_STLP_MSVC_LIB) && (_STLP_MSVC_LIB >= 1400) // hypot is deprecated. # if defined (_STLP_MSVC) # pragma warning (disable : 4996) # elif defined (__ICL) # pragma warning (disable : 1478) # endif #endif _STLP_BEGIN_NAMESPACE // Complex division and square roots. // Absolute value _STLP_TEMPLATE_NULL _STLP_DECLSPEC float _STLP_CALL abs(const complex<float>& __z) { return ::hypot(__z._M_re, __z._M_im); } _STLP_TEMPLATE_NULL _STLP_DECLSPEC double _STLP_CALL abs(const complex<double>& __z) { return ::hypot(__z._M_re, __z._M_im); } #if !defined (_STLP_NO_LONG_DOUBLE) _STLP_TEMPLATE_NULL _STLP_DECLSPEC long double _STLP_CALL abs(const complex<long double>& __z) { return ::hypot(__z._M_re, __z._M_im); } #endif // Phase _STLP_TEMPLATE_NULL _STLP_DECLSPEC float _STLP_CALL arg(const complex<float>& __z) { return ::atan2(__z._M_im, __z._M_re); } _STLP_TEMPLATE_NULL _STLP_DECLSPEC double _STLP_CALL arg(const complex<double>& __z) { return ::atan2(__z._M_im, __z._M_re); } #if !defined (_STLP_NO_LONG_DOUBLE) _STLP_TEMPLATE_NULL _STLP_DECLSPEC long double _STLP_CALL arg(const complex<long double>& __z) { return ::atan2(__z._M_im, __z._M_re); } #endif // Construct a complex number from polar representation _STLP_TEMPLATE_NULL _STLP_DECLSPEC complex<float> _STLP_CALL polar(const float& __rho, const float& __phi) { return complex<float>(__rho * ::cos(__phi), __rho * ::sin(__phi)); } _STLP_TEMPLATE_NULL _STLP_DECLSPEC complex<double> _STLP_CALL polar(const double& __rho, const double& __phi) { return complex<double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); } #if !defined (_STLP_NO_LONG_DOUBLE) _STLP_TEMPLATE_NULL _STLP_DECLSPEC complex<long double> _STLP_CALL polar(const long double& __rho, const long double& __phi) { return complex<long double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); } #endif // Division template <class _Tp> static void _divT(const _Tp& __z1_r, const _Tp& __z1_i, const _Tp& __z2_r, const _Tp& __z2_i, _Tp& __res_r, _Tp& __res_i) { _Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r; _Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i; if (__ar <= __ai) { _Tp __ratio = __z2_r / __z2_i; _Tp __denom = __z2_i * (1 + __ratio * __ratio); __res_r = (__z1_r * __ratio + __z1_i) / __denom; __res_i = (__z1_i * __ratio - __z1_r) / __denom; } else { _Tp __ratio = __z2_i / __z2_r; _Tp __denom = __z2_r * (1 + __ratio * __ratio); __res_r = (__z1_r + __z1_i * __ratio) / __denom; __res_i = (__z1_i - __z1_r * __ratio) / __denom; } } template <class _Tp> static void _divT(const _Tp& __z1_r, const _Tp& __z2_r, const _Tp& __z2_i, _Tp& __res_r, _Tp& __res_i) { _Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r; _Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i; if (__ar <= __ai) { _Tp __ratio = __z2_r / __z2_i; _Tp __denom = __z2_i * (1 + __ratio * __ratio); __res_r = (__z1_r * __ratio) / __denom; __res_i = - __z1_r / __denom; } else { _Tp __ratio = __z2_i / __z2_r; _Tp __denom = __z2_r * (1 + __ratio * __ratio); __res_r = __z1_r / __denom; __res_i = - (__z1_r * __ratio) / __denom; } } void _STLP_CALL complex<float>::_div(const float& __z1_r, const float& __z1_i, const float& __z2_r, const float& __z2_i, float& __res_r, float& __res_i) { _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); } void _STLP_CALL complex<float>::_div(const float& __z1_r, const float& __z2_r, const float& __z2_i, float& __res_r, float& __res_i) { _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); } void _STLP_CALL complex<double>::_div(const double& __z1_r, const double& __z1_i, const double& __z2_r, const double& __z2_i, double& __res_r, double& __res_i) { _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); } void _STLP_CALL complex<double>::_div(const double& __z1_r, const double& __z2_r, const double& __z2_i, double& __res_r, double& __res_i) { _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); } #if !defined (_STLP_NO_LONG_DOUBLE) void _STLP_CALL complex<long double>::_div(const long double& __z1_r, const long double& __z1_i, const long double& __z2_r, const long double& __z2_i, long double& __res_r, long double& __res_i) { _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); } void _STLP_CALL complex<long double>::_div(const long double& __z1_r, const long double& __z2_r, const long double& __z2_i, long double& __res_r, long double& __res_i) { _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); } #endif //---------------------------------------------------------------------- // Square root template <class _Tp> static complex<_Tp> sqrtT(const complex<_Tp>& z) { _Tp re = z._M_re; _Tp im = z._M_im; _Tp mag = ::hypot(re, im); complex<_Tp> result; if (mag == 0.f) { result._M_re = result._M_im = 0.f; } else if (re > 0.f) { result._M_re = ::sqrt(0.5f * (mag + re)); result._M_im = im/result._M_re/2.f; } else { result._M_im = ::sqrt(0.5f * (mag - re)); if (im < 0.f) result._M_im = - result._M_im; result._M_re = im/result._M_im/2.f; } return result; } complex<float> _STLP_CALL sqrt(const complex<float>& z) { return sqrtT(z); } complex<double> _STLP_CALL sqrt(const complex<double>& z) { return sqrtT(z); } #if !defined (_STLP_NO_LONG_DOUBLE) complex<long double> _STLP_CALL sqrt(const complex<long double>& z) { return sqrtT(z); } #endif // exp, log, pow for complex<float>, complex<double>, and complex<long double> //---------------------------------------------------------------------- // exp template <class _Tp> static complex<_Tp> expT(const complex<_Tp>& z) { _Tp expx = ::exp(z._M_re); return complex<_Tp>(expx * ::cos(z._M_im), expx * ::sin(z._M_im)); } _STLP_DECLSPEC complex<float> _STLP_CALL exp(const complex<float>& z) { return expT(z); } _STLP_DECLSPEC complex<double> _STLP_CALL exp(const complex<double>& z) { return expT(z); } #if !defined (_STLP_NO_LONG_DOUBLE) _STLP_DECLSPEC complex<long double> _STLP_CALL exp(const complex<long double>& z) { return expT(z); } #endif //---------------------------------------------------------------------- // log10 template <class _Tp> static complex<_Tp> log10T(const complex<_Tp>& z, const _Tp& ln10_inv) { complex<_Tp> r; r._M_im = ::atan2(z._M_im, z._M_re) * ln10_inv; r._M_re = ::log10(::hypot(z._M_re, z._M_im)); return r; } static const float LN10_INVF = 1.f / ::log(10.f); _STLP_DECLSPEC complex<float> _STLP_CALL log10(const complex<float>& z) { return log10T(z, LN10_INVF); } static const double LN10_INV = 1. / ::log10(10.); _STLP_DECLSPEC complex<double> _STLP_CALL log10(const complex<double>& z) { return log10T(z, LN10_INV); } #if !defined (_STLP_NO_LONG_DOUBLE) static const long double LN10_INVL = 1.l / ::log(10.l); _STLP_DECLSPEC complex<long double> _STLP_CALL log10(const complex<long double>& z) { return log10T(z, LN10_INVL); } #endif //---------------------------------------------------------------------- // log template <class _Tp> static complex<_Tp> logT(const complex<_Tp>& z) { complex<_Tp> r; r._M_im = ::atan2(z._M_im, z._M_re); r._M_re = ::log(::hypot(z._M_re, z._M_im)); return r; } _STLP_DECLSPEC complex<float> _STLP_CALL log(const complex<float>& z) { return logT(z); } _STLP_DECLSPEC complex<double> _STLP_CALL log(const complex<double>& z) { return logT(z); } #ifndef _STLP_NO_LONG_DOUBLE _STLP_DECLSPEC complex<long double> _STLP_CALL log(const complex<long double>& z) { return logT(z); } # endif //---------------------------------------------------------------------- // pow template <class _Tp> static complex<_Tp> powT(const _Tp& a, const complex<_Tp>& b) { _Tp logr = ::log(a); _Tp x = ::exp(logr * b._M_re); _Tp y = logr * b._M_im; return complex<_Tp>(x * ::cos(y), x * ::sin(y)); } template <class _Tp> static complex<_Tp> powT(const complex<_Tp>& z_in, int n) { complex<_Tp> z = z_in; z = _STLP_PRIV __power(z, (n < 0 ? -n : n), multiplies< complex<_Tp> >()); if (n < 0) return _Tp(1.0) / z; else return z; } template <class _Tp> static complex<_Tp> powT(const complex<_Tp>& a, const _Tp& b) { _Tp logr = ::log(::hypot(a._M_re,a._M_im)); _Tp logi = ::atan2(a._M_im, a._M_re); _Tp x = ::exp(logr * b); _Tp y = logi * b; return complex<_Tp>(x * ::cos(y), x * ::sin(y)); } template <class _Tp> static complex<_Tp> powT(const complex<_Tp>& a, const complex<_Tp>& b) { _Tp logr = ::log(::hypot(a._M_re,a._M_im)); _Tp logi = ::atan2(a._M_im, a._M_re); _Tp x = ::exp(logr * b._M_re - logi * b._M_im); _Tp y = logr * b._M_im + logi * b._M_re; return complex<_Tp>(x * ::cos(y), x * ::sin(y)); } _STLP_DECLSPEC complex<float> _STLP_CALL pow(const float& a, const complex<float>& b) { return powT(a, b); } _STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& z_in, int n) { return powT(z_in, n); } _STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const float& b) { return powT(a, b); } _STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const complex<float>& b) { return powT(a, b); } _STLP_DECLSPEC complex<double> _STLP_CALL pow(const double& a, const complex<double>& b) { return powT(a, b); } _STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& z_in, int n) { return powT(z_in, n); } _STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const double& b) { return powT(a, b); } _STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const complex<double>& b) { return powT(a, b); } #if !defined (_STLP_NO_LONG_DOUBLE) _STLP_DECLSPEC complex<long double> _STLP_CALL pow(const long double& a, const complex<long double>& b) { return powT(a, b); } _STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& z_in, int n) { return powT(z_in, n); } _STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a, const long double& b) { return powT(a, b); } _STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a, const complex<long double>& b) { return powT(a, b); } #endif _STLP_END_NAMESPACE

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